The transverse velocities of the gravitational lens system (galaxy plus a 'disturbing star') and their dependences on unkown properties of the source and the deflecting object are discussed. We have derived an analytic expression for the transverse velocity in terms of the velocities of the light source, the gravitational lensing galaxy and the 'disturbing star', and the observer. The results are then further applied to an estimate of the expectation value of the absolute transverse velocity and of the probable time scales of flux changes of the double QSO 0957+561A, B.